Nucleon form factors from quenched lattice QCD with domain wall fermions

We present a quenched lattice calculation of the weak nucleon form factors: vector [$F_V(q^2)$], induced tensor [$F_T(q^2)$], axial vector [$F_A(q^2)$] and induced pseudoscalar [$F_P(q^2)$] form factors. Our simulations are performed on three different lattice sizes $L^3\times T={24}^3\times 32$, ${16}^3\times 32$, and ${12}^3\times 32$ with a lattice cutoff of $a^{-1}\approx 1.3\mathrm{GeV}$ and light quark masses down to about $1/4$ the strange quark mass ($m_{\pi }\approx 390\mathrm{MeV}$) using a combination of the DBW2 gauge action and domain wall fermions. The physical volume of our largest lattice is about $(3.6\mathrm{fm}{)}^3$, where the finite volume effects on form factors become negligible and the lower momentum transfers ($q^2\approx 0.1{\mathrm{GeV}}^2$) are accessible. The $q^2$ dependences of form factors in the low $q^2$ region are examined. It is found that the vector, induced tensor, and axial-vector form factors are well described by the dipole form, while the induced pseudoscalar form factor is consistent with pion-pole dominance. We obtain the ratio of axial to vector coupling $g_A/g_V=F_A(0)/F_V(0)=1.219(38)$ and the pseudoscalar coupling $g_P=m_{\mu }{F}_P(0.88m_{\mu }^2)=8.15(54)$, where the errors are statistical errors only. These values agree with experimental values from neutron $\beta$ decay and muon capture on the proton. However, the root mean-squared radii of the vector, induced tensor, and axial vector underestimate the known experimental values by about 20%. We also calculate the pseudoscalar nucleon matrix element in order to verify the axial Ward-Takahashi identity in terms of the nucleon matrix elements, which may be called as the generalized Goldberger-Treiman relation.